Method for Assessing Performance of Finned Tube Heat Exchanger under Non-uniform Face Velocity

ABSTRACT

A method for assessing and improving the performance of a finned tube heat exchanger under non-uniform face velocity is disclosed. First, a mathematical analysis method of the finned tube heat exchanger under the non-uniform face velocity is established. Second, a heat exchange amount and the heat resistance of the heat exchanger are obtained. Third, a quantitative relation between the non-uniform face velocity distribution and the performance of the finned tube heat exchanger are obtained. Finally, the heat exchange amount and the heat resistance of the heat exchanger are drawn in a rectangular plane coordinate system; and the coordinate system is partitioned in accordance with change rules of the curves, so that a performance assessment diagram of the finned tube heat exchanger under the non-uniform face velocity condition is obtained.

CROSS REFERENCE TO RELATED APPLICATION

This application is based upon and claims priority to Chinese PatentApplication No. 201811551614.3, filed on Dec. 19, 2018. The entiredisclosure of the above-identified application is incorporated herein byreference.

Some references, which may include patents, patent applications, andvarious publications, are cited and discussed in the description of thepresent disclosure. The citation and/or discussion of such references isprovided merely to clarify the description of the present disclosure andis not an admission that any such reference is “prior art” to thedisclosure described herein. All references cited and discussed in thisspecification are incorporated herein by reference in their entiretiesand to the same extent as if each reference was individuallyincorporated by reference.

TECHNICAL FIELD

The disclosure relates to the technical field of heat transferoptimization of heat exchangers, and particularly relates to a methodfor assessing and improving the performance of a finned tube heatexchanger under non-uniform face velocity.

BACKGROUND

Heat exchangers, as an important part in industrial production, arewidely applied to various fields of production and life. In recentyears, along with the development of society and the advancement oftechnology, production and life's requirements on the effectiveness,urgency and reliability of the heat exchanger are increasing; and novelenhanced heat exchange technologies and heat exchanger optimizationdesign methods are continuously applied to the heat exchanger. Suchapproaches as fin optimization, channel design and the like, asconventional technical means, are mainly adopted in the development ofnovel efficient heat exchanger. However, the influence of face velocitydistribution non-uniformity on the performance of the heat exchanger indesign work is ignored in most researches, resulting in greatdifferences between research results and actual effects of the heatexchanger. At present, due to few researches on face velocitynon-uniformity of the finned tube heat exchanger, universal laws havenot been made, causing small guiding significance to design work of theheat exchanger.

In practical work of the heat exchanger, air passes through the heatexchanger under the action of a fan, and face velocity is generallynon-uniform, which is particularly obvious when the fan is perpendicularto the face side of the heat exchanger. In one aspect, non-uniformity ofair side heat flow of the heat exchanger can be caused by the facevelocity non-uniformity, and subsequently, the efficiency of fins can bereduced; and in the other aspect, flow rate of a refrigerant in a tubecan become mismatched with flow velocity of air outside the tube due tothe face velocity non-uniformity, and the overall heat exchangeperformance of the heat exchanger can greatly drop. At present, someshortcomings still exist in researches on the influence of the facevelocity non-uniformity on the performance of the heat exchanger:firstly, instead of qualitative description on the degree of the facevelocity non-uniformity, it merely takes influence of non-uniformitydistribution in fixed forms on the performance of the heat exchangerinto consideration, and regularity researches on influence of thenon-uniformity degree on the performance are in lack; secondly, relatedcalculation models are established on the basis of velocityone-dimensional non-uniformity distribution, and description andprocessing methods of multi-dimensional velocity are not adopted; andthirdly, related researches, which are conducted on the basis of complexmodeling computation or experimental researches, are high in workloadand cannot effectively assess the influence of non-uniform face velocitydistribution on the performance of the heat exchanger. On thebackground, people urgently hope that the influence of the face velocityon the air side heat exchange performance of the heat exchanger can beproved from the view of theoretical derivation; and a method forassessing the influence of the face velocity non-uniformity on theperformance of the finned tube heat exchanger is provided.

Therefore, a heretofore unaddressed need exists in the art to addressthe deficiencies and inadequacies.

SUMMARY

In order to overcome shortcomings of the prior art, the disclosure aimsat providing a method for assessing and improving the performance of afinned tube heat exchanger under non-uniform face velocity; with theapplication of the method, the influence of an air side velocitydistribution mode of the heat exchanger on the performance of the heatexchanger can be intuitively reflected; on the basis of quantitativecalculation, a conventional heat exchanger optimization design method iscorrected, so as to offer guidance to optimization design of the airside of the heat exchanger in one aspect and to provide reference forthe optimization of the refrigerant side of the heat exchanger in theother aspect. Accordingly, the finned tube heat exchanger can beoptimized and designed.

In order to achieve the purposes, the technical scheme provided by theembodiments is as follows.

A quantitative relation formula of the heat exchange coefficient lossfactor, the heat exchange amount loss factor and the heat resistanceincreasing rate along with the velocity deviation factor of the finnedtube heat exchanger under non-uniform velocity is obtained as the finnedtube heat exchanger is equivalent to a multi-flow heat exchanger andbased on theoretical derivation. Finally, the relation formula undergoesimaging processing, so that a performance assessment diagram under thenon-uniform face velocity of the finned tube heat exchanger is obtained;therefore, the heat exchange performance of the entire heat exchangerunder non-uniform velocity can be accurately assessed just depending onthe performance of a single fin under various working conditions; andrelated performance parameters of the heat exchanger under thenon-uniform velocity can be obtained by calculating the performance ofthe heat exchanger under uniform velocity.

In comparison with current research work on the performance of the heatexchanger under non-uniform face velocity, the method provided by thedisclosure has the following advantages.

The performance assessment diagram under the non-uniform face velocityof the finned tube heat exchanger can fill a gap of description andprocessing methods on multi-dimensional velocity non-uniformitydistribution and can be applied to researches on heat exchangers withthe face velocity being in arbitrary distribution; related parameters ofthe performance of the heat exchanger under non-uniform face velocitycan be obtained in the combination of the performance of the heatexchanger under a face velocity uniform distribution situation under acircumstance that the face velocity distribution is known, withoutassistance of complex modeling computation or experimental researches;and the performance assessment diagram under the non-uniform facevelocity of the finned tube heat exchanger is concise and clear and isconvenient to use, and the performance assessment diagram is significantfor design and optimization guidance of the heat exchanger.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate one or more embodiments of thepresent disclosure and, together with the written description, explainthe principles of the disclosure. Wherever possible, the same referencenumbers are used throughout the drawings to refer to the same or likeelements of an embodiment.

FIG. 1 is a schematic diagram of a simplified model of a finned tubeheat exchanger, as a research object, of the disclosure;

FIG. 2 is a performance assessment diagram under the non-uniform facevelocity of the finned tube heat exchanger of the disclosure;

FIG. 3 is a schematic diagram of velocity distribution forms inapplication cases of the disclosure;

FIG. 4 is a comparison diagram of the influence of uniform velocitydistribution on the performance in application cases of the disclosure;

FIGS. 5(a)-5(e) are schematic diagrams of typical face velocitydistribution types in upper triangular distribution, middle triangulardistribution; lower triangular distribution; parabolic distribution andexponential distribution, respectively; and

FIG. 6 is a comparison diagram of the influence of various face velocitydistribution types on the heat exchange performance of the heatexchanger of the disclosure.

DETAILED DESCRIPTION

The present disclosure will now be described more fully hereinafter withreference to the accompanying drawings, in which exemplary embodimentsof the present disclosure are shown. The present disclosure may,however, be embodied in many different forms and should not be construedas limited to the embodiments set forth herein. Rather, theseembodiments are provided so that this disclosure is thorough andcomplete, and will fully convey the scope of the disclosure to thoseskilled in the art. Like reference numerals refer to like elementsthroughout.

The terms used in this specification generally have their ordinarymeanings in the art, within the context of the disclosure, and in thespecific context where each term is used. Certain terms that are used todescribe the disclosure are discussed below, or elsewhere in thespecification, to provide additional guidance to the practitionerregarding the description of the disclosure. For convenience, certainterms may be highlighted, for example using italics and/or quotationmarks. The use of highlighting and/or capital letters has no influenceon the scope and meaning of a term; the scope and meaning of a term arethe same, in the same context, whether it is highlighted and/or incapital letters. It is appreciated that the same thing can be said inmore than one way. Consequently, alternative language and synonyms maybe used for any one or more of the terms discussed herein, nor is anyspecial significance to be placed upon whether a term is elaborated ordiscussed herein. Synonyms for certain terms are provided. A recital ofone or more synonyms does not exclude the use of other synonyms. The useof examples anywhere in this specification, including examples of anyterms discussed herein, is illustrative only and in no way limits thescope and meaning of the disclosure or of any exemplified term.Likewise, the disclosure is not limited to various embodiments given inthis specification.

It is understood that when an element is referred to as being “on”another element, it can be directly on the other element or interveningelements may be present therebetween. In contrast, when an element isreferred to as being “directly on” another element, there are nointervening elements present. As used herein, the term “and/or” includesany and all combinations of one or more of the associated listed items.

It is understood that, although the terms first, second, third, etc. maybe used herein to describe various elements, components, regions, layersand/or sections, these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are only usedto distinguish one element, component, region, layer or section fromanother element, component, region, layer or section. Thus, a firstelement, component, region, layer or section discussed below can betermed a second element, component, region, layer or section withoutdeparting from the teachings of the present disclosure.

It is understood that when an element is referred to as being “on,”“attached” to, “connected” to, “coupled” with, “contacting,” etc.,another element, it can be directly on, attached to, connected to,coupled with or contacting the other element or intervening elements mayalso be present. In contrast, when an element is referred to as being,for example, “directly on,” “directly attached” to, “directly connected”to, “directly coupled” with or “directly contacting” another element,there are no intervening elements present. It is also appreciated bythose of skill in the art that references to a structure or feature thatis disposed “adjacent” to another feature may have portions that overlapor underlie the adjacent feature.

The terminology used herein is for the purpose of describing embodimentsonly and is not intended to be limiting of the disclosure. As usedherein, the singular forms “a,” “an,” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It is further understood that the terms “comprises” and/or“comprising,” or “includes” and/or “including” or “has” and/or “having”when used in this specification specify the presence of stated features,regions, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,regions, integers, steps, operations, elements, components, and/orgroups thereof.

Furthermore, relative terms, such as “lower” or “bottom” and “upper” or“top,” may be used herein to describe one element's relationship toanother element as illustrated in the figures. It is understood thatrelative terms are intended to encompass different orientations of thedevice in addition to the orientation shown in the figures. For example,if the device in one of the figures is turned over, elements describedas being on the “lower” side of other elements would then be oriented onthe “upper” sides of the other elements. The exemplary term “lower” can,therefore, encompass both an orientation of lower and upper, dependingon the orientation of the figure. Similarly, if the device in one of thefigures is turned over, elements described as “below” or “beneath” otherelements would then be oriented “above” the other elements. Theexemplary terms “below” or “beneath” can, therefore, encompass both anorientation of above and below.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which the present disclosure belongs. Itis further understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art and thepresent disclosure, and will not be interpreted in an idealized oroverly formal sense unless expressly so defined herein.

As used herein, “around,” “about,” “substantially” or “approximately”shall generally mean within 20 percent, preferably within 10 percent,and more preferably within 5 percent of a given value or range.Numerical quantities given herein are approximate, meaning that theterms “around,” “about,” “substantially” or “approximately” can beinferred if not expressly stated.

As used herein, the terms “comprise” or “comprising,” “include” or“including,” “carry” or “carrying,” “has/have” or “having,” “contain” or“containing,” “involve” or “involving” and the like are to be understoodto be open-ended, i.e., to mean including but not limited to.

As used herein, the phrase “at least one of A, B, and C” should beconstrued to mean a logical (A or B or C), using a non-exclusive logicalOR. One or more steps within a method may be executed in different order(or concurrently) without altering the principles of the disclosure.

Embodiments of the disclosure are illustrated in detail hereinafter withreference to accompanying drawings. Specific embodiments describedherein are merely intended to explain the disclosure, but not intendedto limit the disclosure.

The method for assessing and improving the performance under non-uniformface velocity of the finned tube heat exchanger provided by thedisclosure is applied to optimization design of the finned tube heatexchanger under the non-uniform face velocity. Firstly, in order tosolve the problem of air side air inlet non-uniformity of the finnedtube heat exchanger under actual working conditions and to simplify aphysical model, shown as FIG. 1, a mathematical analysis method of thefinned tube heat exchanger under the non-uniform face velocity isestablished. On the basis, the influence on the heat exchangeperformance of the multi-channel finned tube heat exchanger under a facevelocity multi-dimensional non-uniform distribution condition is takeninto theoretical analysis, and rules of the influence of an air sidevelocity deviation factor on an average heat exchange coefficient, aheat exchange amount and the heat resistance of the heat exchanger areobtained; therefore, a quantitative relation between the non-uniformface velocity distribution and the performance of the finned tube heatexchanger is obtained. Finally, in accordance with results of thetheoretical analysis, relation curves between the air side velocitydeviation factor and the average heat exchange coefficient, the heatexchange amount and the heat resistance of the heat exchanger are drawnin a rectangular plane coordinate system; and the coordinate system ispartitioned in accordance with change rules of the curves, so that aperformance assessment diagram of the finned tube heat exchanger underthe non-uniform face velocity condition is obtained, shown as FIG. 2.

Specifically, the method comprises the following steps:

1) determining a quantitative relation of face velocity non-uniformityto the air side average heat exchange coefficient of the finned tubeheat exchanger;

(1) a quantitative relation between face velocity linear distributionand the air side average heat exchange coefficient of the finned tubeheat exchanger; a relation between heat exchanger air side Nusseltnumber Nu and Reynolds number Re can be represented as:

Nu=cRe^(m)

wherein,

Nu=hD/λ

Re=uD/v

a relation between a heat exchanger coefficient h and a flow velocity ucan be represented as:

h(u)=ku ^(m)

a taylor expansion of the relation formula can be represented as:

${h(u)} = {{h\left( u_{0} \right)} + {{h^{\prime}\left( u_{0} \right)}\left( {u - u_{0}} \right)} + {\frac{1}{2!}{h^{''}\left( u_{0} \right)}\left( {u - u_{0}} \right)^{2}} + {\frac{1}{3!}{h^{\prime\prime\prime}\left( u_{0} \right)}\left( {u - u_{0}} \right)^{3}} + \ldots + {\frac{1}{n!}{h^{(n)}\left( u_{0} \right)}} + {R_{n}(u)}}$

a basic relation formula of the influence of the non-uniform facevelocity on the heat exchange performance is represented as:

h(u _(a) +Δu)+h(u _(a) −Δu)−2h(u _(a))=h″(u _(a))Δu ² =m(m−1)ku ^(m-2)Δu ²

change in the heat exchange coefficient of the heat exchanger caused byface velocity non-uniformity is represented as:

${\Delta \; h} = {{h_{uniform} - h_{nonuniform}} = {\frac{{t\left( {t + 1} \right)}\left( {{2t} + 1} \right)}{6n}{m\left( {1 - m} \right)}k\; \Delta \; u^{2}u_{a}^{m - 2}}}$

a heat exchange coefficient loss factor σ is represented as:

$\sigma = {\frac{\Delta \; h}{h_{uniform}} = {{\frac{n^{2} - 1}{6n^{2}}{m\left( {- m} \right)}\omega^{2}} = {\frac{1}{6}{m\left( {1 - m} \right)}\omega^{2}\mspace{14mu} \left( {\omega_{j} \neq 0} \right)}}}$

wherein,

Δ u = (u_(max) − u_(min))/n u_(a) = (u_(max) + u_(min))/2$\omega = {\frac{u_{\max} - u_{\min}}{u_{\max} + u_{\min}} = \frac{\left( {u_{\max} - u_{\min}} \right)/2}{u_{a}}}$n = 2t + 1 $\frac{n^{2} - 1}{n^{2}} \approx 1$

(2) a quantitative relation between arbitrary face velocity distributionand the air side average heat exchange coefficient of the finned tubeheat exchanger;

when face velocity is in arbitrary distribution, the entire face sidecan be divided into a plurality of small blocks; provided that airvelocity is in linear change in the plurality of small blocks, anoverall heat exchange coefficient loss factor σ is obtained, representedas:

$\sigma = {\frac{\Delta \; h}{h_{uniform}} = {1 - {\sum\limits_{j}{\frac{A_{j}}{A_{f}}\left( {1 - \sigma_{j}} \right)ɛ_{h\text{-}j}}}}}$

wherein,

$\sigma_{j}=={\frac{1}{6}{m\left( {1 - m} \right)}\omega_{j}^{2}}$$ɛ_{h\text{-}j} = {\frac{h_{{uniform}\text{-}j}}{h_{unform}} = \left( \frac{u_{a\text{-}j}}{u_{a}} \right)^{m}}$

2) determining a quantitative relation of the face velocitynon-uniformity to the heat exchange amount of the finned tube heatexchanger;

the heat exchange amount of a unit channel can be represented as:

q=h(u)AΔT

wherein, A stands for a heat exchange area in heat exchange channels,and ΔT is a heat exchange temperature difference. The various channelsare the same in heat exchange area A. It is regarded that the variousunits of heat exchange channels are the same in heat exchangetemperature difference ΔT when a velocity deviation amount is quitesmall, namely a velocity deviation factor ω is close to 0; and the heatexchange amount is mainly determined by the heat exchange coefficient h.

(1) a quantitative relation of face velocity linear distribution to theair side heat exchange amount of the finned tube heat exchanger;

when a velocity deviation amount is quite small under a face velocitylinear change condition, the heat exchange amount can be represented as:

$Q_{nonuniform} = {{A\; \Delta \; T{\sum\limits_{1}^{t}{{m\left( {m - 1} \right)}{ki}^{2}\Delta \; u^{2}u_{a}^{m\text{-}2}}}} + {\left( {{2t} + 1} \right){h\left( u_{a} \right)}A\; \Delta \; T}}$

under equivalent flow, the heat exchange amount of the overall machine(the heat exchanger) under uniform face velocity can be represented as:

Q _(uniform)=(2t+1)h(u _(a))AΔT

under a face velocity linear distribution condition, a heat exchangeamount loss factor η can be represented as:

$\eta = {\frac{\Delta \; Q}{Q_{uniform}} = {{\frac{t\left( {t + 1} \right)}{6}{m\left( {m - 1} \right)}u_{a}^{- 2}\Delta \; u^{2}} = {\frac{n^{2} - 1}{6n^{2}}{m\left( {m - 1} \right)}\omega^{2}}}}$

the various channels are different in heat exchange temperaturedifference ΔT when velocity deviation is quite large, namely thevelocity deviation factor ω is a relatively large value. The entire faceside can be equally divided into nt pieces of cells, and a heat exchangeamount loss factor ηj in each cell can be obtained as a velocitydeviation factor ωj on the face side of each heat exchange cell is smallenough; and furthermore, the heat exchange amount loss factor η of theentire heat exchanger under a face velocity linear distributioncircumstance can be obtained in accordance with the relation of the heatexchange amount:

$\begin{matrix}{\eta = {\frac{\Delta \; Q}{Q_{uniform}} = \frac{\sum\limits_{j}{\Delta \; Q_{j}}}{n_{t}Q_{{uniform}\text{-}{cell}}}}} \\{= {\frac{A_{j}}{A_{f}}{\sum\limits_{j}\frac{Q_{{uniform}\text{-}{cell}} - Q_{j}}{Q_{{uniform}\text{-}{cell}}}}}} \\{= {\sum\limits_{j}{\frac{A_{j}}{A_{f}}\left\lbrack {1 - {\left( {1 - \eta_{j}} \right)\frac{Q_{{uniform}\text{-}j}}{Q_{uniform}}}} \right\rbrack}}} \\{= {1 - {\sum\limits_{j}{\frac{A_{j}}{A_{f}}\left( {1 - \eta_{j}} \right)ɛ_{Q\text{-}j}}}}}\end{matrix}$

wherein

$\eta_{j}=={\frac{1}{6}{m\left( {1 - m} \right)}\omega_{j}^{2}}$$ɛ_{Q\text{-}j} = {\frac{Q_{{uniform}\text{-}j}}{Q_{{uniform}\text{-}{cell}}} = {\left( \frac{u_{a\text{-}j}}{u_{a}} \right)^{m}\frac{\Delta \; T_{{uniform}\text{-}j}}{\Delta \; T_{{uniform}\text{-}{cell}}}}}$

(2) a quantitative relation of face velocity arbitrary distribution tothe air side heat exchange amount of the finned tube heat exchanger;

as a processing method of the heat exchange coefficient loss factor σ,the heat exchange amount loss factor η under a face velocity arbitrarydistribution condition is represented as:

$\eta = {\frac{\Delta \; Q}{Q_{uniform}} = {1 - {\sum\limits_{j}{\frac{A_{j}}{A_{f}}\left( {1 - \eta_{j}} \right)ɛ_{Q\text{-}j}}}}}$

3) determining a quantitative relation of the face velocitynon-uniformity to the heat resistance of the finned tube heat exchanger;a heat-conduction control equation is represented as:

−∇·q=0

by multiplying temperature T by two sides of the control equation, arelation, which is shown as the follows, can be obtained:

q·∇T·∇·(qT)=0

in combination with a Gaussian divergence law, a relation, which isshown as the follows, can be obtained:

${\int\limits_{V_{1}}{\left\lbrack {{q \cdot {\nabla T}} - {\nabla{\cdot ({qT})}}} \right\rbrack {dV}_{1}}} = {{{\int\limits_{V_{1}}{q \cdot {\nabla{TdV}_{1}}}} - {\int\limits_{A_{1}}{{({qT}) \cdot n_{1}}{dA}_{1}}}} = 0}$

entranspy dissipation of heat conduction can be represented as:

$G_{{dis}\text{-}{cond}} = {{\int\limits_{V_{1}}{{\lambda \left( {\nabla T} \right)}^{2}{dV}_{1}}} = {- {\int\limits_{A_{1}}{{({qT}) \cdot n_{1}}{dA}_{1}}}}}$

a convective heat control equation can be represented as:

ρc(u·∇T)=−∇·q+ϕ

by multiplying temperature T by two sides of the control equation, arelation, which is shown as the follows, can be obtained:

${\frac{1}{2}\rho \; {c\left\lbrack {u \cdot {\nabla(T)^{2}}} \right\rbrack}} = {{{- \nabla} \cdot ({qT})} + {q \cdot {\nabla T}}}$

by integrating an entire convective region, a relation, which is shownas the follows, can be obtained:

${{\int_{V_{2}}{\frac{1}{2}\rho \; {c\left\lbrack {u \cdot {\nabla(T)^{2}}} \right\rbrack}{dV}_{2}}} = {{- {\int_{V_{2}}{{\nabla{\cdot ({qT})}}{dV}_{2}}}} + {\int_{V_{2}}{q \cdot {\nabla{TdV}_{2}}}}}}\ $

in combination with a Gaussian divergence law, entranspy dissipation ofa convective part, represented as the following formula, can beobtained:

${G_{{dis}\text{-}{conv}} = {{\int_{V_{2}}{{\lambda \left( {\nabla T} \right)}^{2}{dV}_{2}}} = {{- {\int_{A_{2}}{\left( {\frac{1}{2}\rho \; {cT}^{2}} \right){u \cdot n_{2}}{dA}_{2}}}} - {\int_{A_{2}}{{({qT}) \cdot n_{2}}{dA}_{2}}}}}}\ $

total entranspy dissipation can be represented as:

$G_{dis} = {{G_{{dis}\text{-}{cond}} + G_{{dis}\text{-}{conv}}} = {\sum\limits_{i = 1}^{n}\left( {{\frac{1}{2}c_{i}m_{i}T_{{in}\text{-}1}^{2}} - {\frac{1}{2}c_{i}m_{i}T_{{out}\text{-}i}^{2}}} \right)}}$

in accordance with definition of generalized heat resistance, the heatresistance of the multi-flow heat exchanger can be represented as:

$R = {{G_{dis}/Q^{2}} = {\frac{1}{\left( {1 - \eta} \right)^{2}Q_{uniform}}{\sum\limits_{i = 1}^{n}{\frac{A_{i}}{A_{f}}\left( {1 - \eta_{i}} \right)ɛ_{Q - 1}T_{i}}}}}$

wherein,

T _(i)=(T _(in-i) +T _(out-i))/2

a non-uniform heat resistance increasing factor ψ is defined as:

$\psi = {\frac{R_{nonuniform}}{R_{uniform}} = {1 + {\left( {\frac{1}{1 - \eta} - 1} \right){\frac{T_{in}}{T_{uniform}}.}}}}$

Finally, a calculating relation formula, obtained from theoreticalderivation, on the influence of the face velocity non-uniformity on theperformance of the heat exchanger is reflected in a rectangular planecoordinate system. Based upon results, it is indicated that theinfluence of the non-uniform face velocity on the performance of theheat exchanger is quite small within a certain velocity deviation range;the heat exchange performance of the heat exchanger, under the influenceof the non-uniform face velocity, drops along with increase in velocitydeviation; and the heat exchange performance of the heat exchanger dropsexponentially when velocity deviation reaches a certain degree. Based onthe conclusion, the coordinate system is divided into three regions, sothat a performance assessment diagram under the non-uniform facevelocity of the finned tube heat exchange is formed; and in accordancewith the diagram, the influence of various face velocity distribution onthe performance of the heat exchanger can be assessed.

The disclosure will be described based upon two cases as follows.

Case I: the performance of a multi-loop multi-row-tube V-shaped heatexchanger of a 50 kW air source heat pump cold (hot) water set isassessed under a non-uniform face velocity condition.

Based upon numerical simulation, the performance of the multi-loopmulti-row-tube V-shaped heat exchanger of the 50 kW air source heat pumpcold (hot) water set under non-uniform face velocity is obtained: undersuch conditions that air side average air velocity is 2 m/s, velocitydistribution is in linear distribution (shown as FIG. 3) and velocitydeviations are respectively 0.25, 0.5 and 0.75, heat exchange amountsdrop by 0.267%, 3.2% and 11.33% in comparison with the uniform facevelocity condition.

The disclosure, in assessment of the case, specifically comprises thefollowing implementation steps:

(1) in accordance with a relation formula of Nu number of air side finsas well as structural parameters of the fins, deducing out outlettemperatures of the fins under various face velocities of correspondingworking conditions;

(2) in accordance with dimension parameters of the heat exchanger,calculating velocity distribution corresponding to various velocitydeviations when average air velocity is 2 m/s;

(3) depending on velocity distribution situation of each group,reasonably blocking the heat exchanger;

(4) in accordance with quantitative calculating relation formula of theair side heat exchange amount loss of the finned tube heat exchangerunder face velocity non-uniform distribution, and in combination withthe steps (1), (2) and (3), calculating a loss proportion of heatexchange amounts of various velocity deviations;

(5) drawing a diagram in accordance with data obtained in the step (4);and

(6) plotting points in the diagram drawn in the step (5) in accordancewith results of numerical simulation computation and conductingcomparison.

Based on comparison results, it is indicated that heat exchange amountlosses, which are calculated depending on the theory of the disclosure,are respectively 0.29%, 2.89% and 5.25% when velocity deviations are0.25, 0.5 and 0.75, and in comparison with simulation results of theheat exchanger (taking a heat exchanger of the refrigerant side intoconsideration), errors are respectively 2.0%, 3.1% and 53.7%. It can beregarded that the assessment method provided by the disclosure isrelatively high in reliability since non-uniform velocity distributionholds a dominant position in the influence on the heat exchange of therefrigerant side when the velocity deviations are overlarge. Based uponthe case, it is indicated that with the application of the assessmentmethod of the disclosure, the performance calculation of the heatexchanger under the non-uniform face velocity condition can be convertedinto the performance calculation under the uniform velocity condition;therefore, the precision of calculating actual working conditions of theheat exchanger is enhanced, and a calculating process is simplified.

Case II: in the actual work of the heat exchanger, distribution type ofthe face velocity depends on relative positions of the fan and the heatexchanger. For example, the face velocity generally appears as parabolicdistribution when the fan faces the face side of the heat exchanger; theface velocity generally appears as upper triangular distribution whenthe action of a base (such as the ground) exists; and the face velocityappears as upper triangular distribution when the fan is arranged at thetop. Common air velocity distribution types are shown as FIGS. 5(a),5(b), 5(c), 5(d) and 5(e), wherein the upper triangular distribution,lower triangular distribution and middle triangular distribution resultin different influences on the actual performance of the heat exchanger,which is mainly because the three arrangement modes can result indifferent influences on the flowing and heat exchange of the refrigerantside under a specific channel arrangement mode. Under a circumstance ofnot taking the heat exchange of the refrigerant side into consideration,influences of the three velocity distribution types on the air side heatexchange performance are consistent. In several typical face velocitydistribution types shown as FIGS. 5(a), 5(b), 5(c), 5(d) and 5(e),exponential distribution velocity achieves the maximum dispersiondegree, followed by triangular distribution, and then parabolicdistribution velocity, referring to FIG. 6 for calculating results.Based upon the figures, the various face velocity distribution typeskeep great differences in influence on the heat exchange performance ofthe heat exchanger under a circumstance that an air volume is a definedvalue. In comparison with uniform face velocity distribution, parabolicvelocity distribution causes the minimum heat exchange performancedegradation degree, followed by triangular distribution, and thenexponential distribution. Based upon results of theoretical calculation,under prescribed working conditions, heat exchange coefficientnon-uniformity losses, which are caused by parabolic velocitydistribution, triangular velocity distribution and exponential velocitydistribution, are respectively 2.1%, 2.7% and 6.7%, heat exchange amountnon-uniformity losses are respectively 5.6%, 7.4% and 13.3%, and heatresistance increasing rates are respectively 5.8%, 7.8% and 15.0%;therefore, it is indicated that the face velocity non-uniformity causesobvious influence on the actual heat exchange performance of the heatexchanger, and various face velocity distribution types keep greatdifference in influence on the performance of the heat exchanger; inactual performance calculation of the heat exchanger, calculationresults are not accurate when the influence of the velocitynon-uniformity distribution is not taken into consideration; andignoring the influence of the heat exchange of the refrigerant side, theinfluence of the face velocity non-uniformity on the heat exchangeperformance of the heat exchanger is determined by the dispersion degreeof the velocity, and the heat exchange performance loss becomes moreobvious as the dispersion degree of the velocity is greater.

The foregoing description of the exemplary embodiments of the presentdisclosure has been presented only for the purposes of illustration anddescription and is not intended to be exhaustive or to limit thedisclosure to the precise forms disclosed. Many modifications andvariations are possible in light of the above teaching.

The embodiments were chosen and described in order to explain theprinciples of the disclosure and their practical application so as toactivate others skilled in the art to utilize the disclosure and variousembodiments and with various modifications as are suited to theparticular use contemplated. Alternative embodiments will becomeapparent to those skilled in the art to which the present disclosurepertains without departing from its spirit and scope. Accordingly, thescope of the present disclosure is defined by the appended claims ratherthan the foregoing description and the exemplary embodiments describedtherein.

What is claimed is:
 1. A method for assessing and improving theperformance of a finned tube heat exchanger under non-uniform facevelocity, wherein the method comprises: 1) determining a quantitativerelation of face velocity non-uniformity to an air side average heatexchange coefficient of the finned tube heat exchanger; (a) aquantitative relation between face velocity linear distribution and theair side average heat exchange coefficient of the finned tube heatexchanger is prescribed within an expression formula:${\sigma = {\frac{\Delta \; h}{h_{uniform}} = {\frac{1}{6}{m\left( {1 - m} \right)}\omega^{2}}}};$σ stands for a heat exchange coefficient loss factor, and Δh is changeof the heat exchange coefficient of the heat exchanger caused by of facevelocity non-uniformity, satisfying a formula:${{\Delta \; h} = {{h_{uniform} - h_{nonuniform}} = {\frac{{t\left( {t + 1} \right)}\left( {{2t} + 1} \right)}{6n}{m\left( {1 - m} \right)}\; k\; \Delta \; u^{2}u_{a}^{m - 2}}}};$wherein, h_(uniform) form distribution and h_(nonuniform) distributionare heat exchange coefficients of the heat exchanger under uniform airvelocity and non-uniform air velocity; m is a coefficient in a relationof Nu: Nu=cRe^(m); n stands for the quantity of heat exchange channels;and k is a constant; ω is a defined dimensionless parameter velocitydeviation factor, satisfying a relation:${\omega = {\frac{u_{\max} - u_{\min}}{u_{\max} + u_{\min}} = \frac{\left( {u_{\max} - u_{\min}} \right)/2}{u_{a}}}},$wherein u_(max), u_(min) and u_(a) respectively stand for the maximumvalue, the minimum value and an average value of the corresponding airvelocity of a researched face side, satisfying relations:${{\Delta \; u} = {\left( {u_{\max} - u_{\min}} \right)/n}},{u_{a} = {\left( {u_{\max} + u_{\min}} \right)/2}},{{n = {{{2t} + {1\mspace{14mu} {and}\mspace{14mu} \frac{n^{2} - 1}{n^{1}}}} \approx 1}};}$(b) a quantitative relation between face velocity arbitrary distributionand the air side average heat exchange coefficient of the finned tubeheat exchanger is prescribed within an expression formula:${\sigma = {\frac{\Delta \; h}{h_{uniform}} = {1 - {\sum\limits_{j}{\frac{A_{j}}{A_{f}}\left( {1 - \sigma_{j}} \right)ɛ_{h - j}}}}}};$wherein, σ_(j), ω_(j) and h_(uniform-j) respectively stand for a heatexchange coefficient loss factor, a velocity deviation factor and a heatexchange factor corresponding to uniform velocity of the j<th> heatexchange unit (provided that the heat exchange units are in lineardistribution); ε_(h-j) is a heat exchange coefficient discrete factor,satisfying a relation:${ɛ_{h - j} = {\frac{h_{{uniform}\text{-}j}}{h_{uniform}} = \left( \frac{u_{a - j}}{u_{a}} \right)^{m}}};$2) determining a quantitative relation of the face velocitynon-uniformity to heat exchange amount of the finned tube heatexchanger, prescribed within an expression formula:${\eta = {\frac{\Delta \; Q}{Q_{uniform}} = {1 - {\sum\limits_{j}{\frac{A_{j}}{A_{f}}\left( {1 - \eta_{j}} \right)ɛ_{Q - j}}}}}};$wherein, η is a heat exchange amount loss factor, satisfying a relation:${\eta_{j}=={\frac{1}{6}{m\left( {1 - m} \right)}\omega_{j}^{2}}},$ε_(Q-j) stands for a heat exchange amount deviation factor, satisfying arelation:${ɛ_{Q - j} = {\frac{Q_{{uniform}\text{-}j}}{Q_{{uniform}\text{-}{cell}}} = {\left( \frac{u_{a - j}}{u_{a}} \right)^{m}\frac{\Delta \; T_{{uniform}\text{-}j}}{\Delta \; T_{{uniform}\text{-}{cell}}}}}};$Q_(uniform-j) and ΔT_(uniform-j) respectively stand for a heat exchangeamount and a log mean temperature difference of the j<th> unit under auniform velocity distribution condition; and Q_(uniform-cell) andΔT_(uniform-cell) respectively stand for a heat exchange amount and alog mean temperature difference corresponding to each cell under uniformvelocity after the heat exchanger is equally divided; 3) determining aquantitative relation of the face velocity non-uniformity to the heatresistance of the finned tube heat exchanger, prescribed within anexpression formula:${\psi = {\frac{R_{nonuniform}}{R_{uniform}} = {1 + {\left( {\frac{1}{1 - \eta} - 1} \right)\frac{T_{in}}{T_{uniform}}}}}};$wherein, Ψ stands for an increasing rate of the heat resistance;R_(uniform) and R_(nonuniform) respectively stand for air side heatresistance of the heat exchanger corresponding to uniform velocity andair side heat resistance of the heat exchanger corresponding tonon-uniform velocity; and T_(in) and T_(uniform) respectively stand forair side inlet temperature of the heat exchanger and air sideinlet/outlet arithmetic mean temperature under an average air velocitycondition; 4) calculating relation formulas on the influence of theobtained face velocity non-uniformity on performance, namely the airside average heat exchange coefficient, the heat exchange amount and theheat resistance, of the finned tube heat exchanger, and reflecting therelation formulas in a rectangular plane coordinate system, whereinbased upon results, it is indicated that the influence of thenon-uniform face velocity on the performance of the heat exchanger isquite small within a certain velocity deviation range; the heat exchangeperformance of the heat exchanger, under the influence of thenon-uniform face velocity, drops along with increase in velocitydeviation; and the heat exchange performance of the heat exchanger dropsexponentially when velocity deviation reaches a certain degree; and 5)dividing the coordinate system into three regions, namely a performancestable region, a performance degradation region and a performanceserious degradation region based upon conclusion obtained in the step4), so that a performance assessment diagram under the non-uniform facevelocity of the finned tube heat exchanger is defined; and assessinginfluence of various face velocity distribution on the performance ofthe finned tube heat exchanger on the basis of the diagram.
 2. Themethod for assessing and improving the performance of the finned tubeheat exchanger under non-uniform face velocity of claim 1, wherein therectangular plane coordinate system takes the velocity deviation factorω as transverse coordinate, and the heat exchange coefficient lossfactor σ, the heat exchange loss factor η and the heat resistanceincreasing rate Ψ as vertical coordinates.
 3. The method for assessingand improving the performance of the finned tube heat exchanger undernon-uniform face velocity of claim 2, wherein the influence of the facevelocity non-uniformity on the performance of the heat exchanger isquite small when the velocity deviation is within 20-30%; the influenceof the face velocity non-uniformity on the performance of the heatexchanger becomes obvious along with increase in velocity variation; andthe performance of the heat exchanger is presented in exponentialattenuation along with further increase in the velocity deviation. 4.The method for assessing and improving the performance of the finnedtube heat exchanger under non-uniform face velocity of claim 3, whereinheat exchange performance of the entire heat exchanger under non-uniformvelocity can be accurately assessed just depending on the performance ofa single fin under various working conditions, so that relatedperformance parameters of the heat exchanger under the non-uniformvelocity can be obtained by calculating the performance of the heatexchanger under uniform velocity.
 5. The method for assessing andimproving the performance of the finned tube heat exchanger undernon-uniform face velocity of claim 4, wherein the rationality of facevelocity distribution can be inspected, so as to offer certain guidingsuggestions for the velocity of the heat exchanger and the arrangementof internal parts, and to provide reference for the optimization of theshape of the heat exchanger.